Question

answer the following by using formula:

if x+y=2½ and xy=1, find x-y and x³-y³
​

Answer 1

Answer:

Formula :-

(x+y)^3 = x^3+y^3+3.x.y.(x+y).

or, (x+y)^3 = 2 + 3×1×(x+y). , (x+y) = p.

or, f(p) = p^3 -3p -2 = 0.

f(-1)= (-1)^3–3×(-1) -2 or, -1 +3–2 = 0.

Thus, p+1 is a factor of f(p).

p ^3 - 3.p - 2 = 0.

or, p^2.(p+1) -p(p+1)-2.(p+1)=0.

or, (p+1).{p^2 -p -2} = 0.

or, (p+1).(p-2).(p+1)=0.

or, p = -1 , 2.

Thus , the value of (x+y) = -1 , 2. Answer.